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A popular lottery game takes 80 balls, numbered 1 through 80, places the balls in a hopper which then mixes them up throughly. 20 of these balls are taken out. The simplest way for a person to play is to pay $1 and pick one number. If the player's number is one of the 20 chosen, they win back $3. Let X=the net amount gained on a single play of the game.
a) Compute the expected value of X and explain what this means for the player
b) Is this game "fair"? Explain why or why not.
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